Vector Algebra Class 12 Formulas

Vectors are mathematical entities that have both magnitude and direction. Vector algebra class 12 formulas are useful in performing numerous arithmetic operations on the same vector and between two vectors. Owing to the different kinds of symbols used in the Vector Algebra Class 12 Formulas these operations often seem confusing to students. But with proper understanding and memorization of vector algebra class 12 formulas, it will become easy for students to solve various problems based on them. This article aims at covering the important list of Vector Algebra Class 12 Formulas along with relevant examples and applications.

List of Vector Algebra Class 12 Formulas

Given below is a summarized list of vector algebra class 12 formulas:

• Position vector of a point A(a, b, c) is given as  $\overrightarrow {OP} = \overrightarrow {a} =\widehat ai+\hat bj+\hat ck$, and its magnitude is given by $|(\overrightarrow {OP})|= |\overrightarrow a| = √(a^2 + b^2 + c^2)$
• The relationship between the magnitude (r), direction ratios (a, b, c) and direction cosines (l, m, n) of any vector can be seen as: l = a/r , m = b/r , c = n/r
• For a given vector a; the unit vector in the direction of is $\hat a = \overrightarrow {a}/|(\overrightarrow {a})|$
• The scalar product of two given vectors having angle θ between them is defined as $\overrightarrow {a} . \overrightarrow {b} =|\overrightarrow {a}|.|\overrightarrow {b}|Cosθ$
• If θ is the angle between two vectors $\overrightarrow a$ and $\overrightarrow b$, then their cross product is given as$\overrightarrow {a} × \overrightarrow {b} =|\overrightarrow {a}|.|\overrightarrow {b}| Sinθ \hat n$

Applications of Vector Algebra Class 12 Formulas

The vector algebra class 12 formulas have their applications in solving various real-world problems. Some of them are explained below:

• In physics and engineering, scalar and vector quantities and their algebraic formulas are encountered quite often. Some of the examples of scalar quantities are time, length, mass, speed, volume, while that of the vector quantities are velocity, weight, etc.

• Vector algebra formulas are useful in calculating the amount of solar power generated from solar panels.
• These formulas are applied in space science to calculate the distance and angles between the panels of the satellites.
• In civil engineering, vector algebra class 12 formulas are helpful in performing calculations for building beams and structures.

Tips to Memorize Vector Algebra Class 12 Formulas

Students will find the below-mentioned tips helpful in remembering the vector algebra class 12 formulas:

Logical Understanding: It is necessary to have a clear understanding of the logic behind the formula before moving on to solving problems based on them. Writing down the formula steps and understanding its derivation is also useful.

Practicing: Students should practice all the solved examples and problems in textbooks to learn how to apply vector algebra class 12 formulas in various contexts.

Study Material: Students can download formula sheets and set the formula images as wallpapers on their mobiles or tablets to ensure a quick revision.

Vector Algebra Class 12 Formulas Examples

Example: What will be the unit vector in the direction of the vector $\overrightarrow a = \hat i+3\hat j+\hat k$

Solution: The unit vector towards the direction of a vector a is given by  $\hat a = \overrightarrow {a}/|(\overrightarrow {a})|$

Magnitude of a is  $|\overrightarrow {a}| =\sqrt 1^2+3^2+1^2$

= (11)

$\hat a=1/\sqrt 11.(\hat i+3\hat j+\hat k) = 1/\sqrt 11\hat i+3/\sqrt 11\hat j+1/\sqrt 11\hat k$ 

Students can download the printable Maths Formulas Class 12 sheet from below.

 

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